1. Field of Invention
This invention relates to a computer-implemented information system and software for calculating settlement prices for Model Option Contracts.
2. Background of the Invention
Options
Option contracts give the holder a right to buy or sell property at a specified price, called the strike or exercise price, within a given period of time. The life of an option is called the contract's term and is determined by the expiration date of the contract. The payment that is exchanged for this right is called the option premium. If the option holder does not exercise his right prior to the contract's expiration, the option expires worthless.
Having the right but not the obligation to buy or sell property at some prespecified price is valuable. This is why option buyers are willing to pay option sellers a premium for this right. Since options derive their value from the price of the underlying assets they are considered derivatives.
The Value of an Option
An option's value can be thought of as having two primary components. The intrinsic value is the value that an investor would get if she immediately exercised the option. This is the difference between the current price and the exercise price and is also described as “moneyness.” If the option has a positive intrinsic value, it is said to be “in-the-money.” “Deep in-the-money” options refer to options that have a substantially positive intrinsic value.
The second component of an option's value results from how likely and in what direction the intrinsic value of the option is expected to change over the life of option. This is known as the “time value” of an option, and it is a function of the underlying asset's propensity to change in value and the remaining life of an option.
Although many options expire without value, most options that are in-the-money are bought or sold, rather than exercised. This is because exercising an option early forfeits the remaining time value of the option. Also, exercising an option and converting it into the underlying property destroys the financial leverage that options enable.
Financial Leverage
Options are beneficial because they allow the holder to gain financial leverage by buying just the portion of the underlying property that the holder believes is desirable. For example, a speculator who believes that a particular stock will rise to $60 within the next three months from its current price of $50 has a choice of buying the underlying stock or call options on the stock.
Assuming that the speculator has $5,000 to invest and a three-month option to buy one share at a strike price of $50 cost $3.58, the speculator can buy either 100 shares of the stock or purchase 1,396 options to buy the stock. The call options are significantly cheaper than the stock because they are only valuable if the stock price increases above $50 per share during the next three months.
If the speculator is correct and the stock price increases to $60, she will make $1,000 if she purchases the stock. She will make $8,962 if she purchases the options ($60−$50=$10 per share increase times $1,396 options=$13,960 less the option premium of $4,998). Thus, it can be seen that it is much more financially efficient for the speculator to buy options than to buy the underlying stock.
Option Usage
Exchanges facilitate the trading of options on stock, commodities, currencies, and debt instruments. An exchange can be a physical location or an electronic mechanism where trading takes place. Exchanges may be set up and function in many different ways. For example, they can act as a counterparty between buyers and sellers or they can merely provide information that enables buyers and sellers to trade directly with one another.
Although options can be traded directly between two individuals or companies, this rarely happens in practice. This is because exchanges assist in the price discovery process and provide a valuable role in minimizing credit risk.
Options are used in many different ways. Speculators use options to bet on the underlying property increasing or decreasing in value over some specified period of time. Assuming a speculator believes that the underlying property's price will decrease, she may purchase a put option, giving her the right to sell that property to the option seller at a pre-specified price. Conversely, if she believes that the price will increase, she may desire to purchase a call option that will give her the right to buy the property from the option seller at a pre-specified price.
Many investors use options to hedge or offset the risk of some component of their portfolio. For example, a stockholder who is concerned that stock prices may fall dramatically might buy put options and sell call options to limit the potential loss of value. Similarly, manufacturers may desire to hedge price increases or decreases associated with their raw material inventories.
Options Classified by Exercise Features
There are three main ways in which the exercise feature of options is generally structured. American style options enable the holder to exercise the option at any point prior to the expiration date. European style options only enable the holder to exercise the option on the expiration date. Burmudian options may be exercised at any one of various pre-set points during the life of the option.
Options as Compensation
Companies routinely grant options as compensation (i.e. compensation options) in exchange for work or other services. This is commonly referred to as an “incentive stock option” since it is often granted to corporate managers and employees as a means of motivating them to achieve certain financial and operational objectives. Compensation options are usually granted at a strike price that is at the price of the underlying stock on the grant date and these options often vest over a period of future employment such as three or four years. In addition, incentive stock options usually have much longer terms than exchange traded stock options.
Option Pricing Models
A number of mathematical models have been developed to determine the “theoretical value” of an option. However, it is important to point out that the “theoretical value” of an option is not the same thing as the “actual value” of an option. For example, the theoretical value of a call option is a mathematical value that is derived from making certain assumptions about the performance of the reference asset and the risk free rate of return. The actual value is the value that the holder can generate from the option either by selling the option, if that is contractually possible, or by paying the option seller the strike price and forcing delivery of the reference asset. The problem for option users is that the theoretical value of an option and the actual value of an option are usually not the same.
The first of these mathematical models to achieve widespread acceptance was the Black and Scholes Option Pricing Model which was introduced in 1973. This model is predicated upon the following assumptions: the stock pays no dividends; European exercise terms are used; markets are efficient; no commissions are charged; interest rates are known and constant; and returns are lognormally distributed. Since each of these assumptions can be debated, this model has been modified over time, and other models have been developed to correct certain perceived weaknesses of the Black and Scholes Model.
For example, the Binomial Model breaks down the time to the expiration of an option into discrete intervals. At each interval, the stock is assumed to increase or decrease by a certain amount based on its volatility and time to expiration. In effect, this produces a tree of potential stock prices over the life of the option with each branch representing a possible path that the stock price could take during the remaining life of the option. Probabilities are then applied to each path to produce the expected value of the option.
Although a number of option price models have been developed since the Black and Scholes Model, this Model is still widely used due to the fact that it can be calculated faster than some of the newer models that require far more calculations. Calculation speed is critically important because market prices can change very quickly, and even the most advanced computers may have trouble calculating theoretical values fast enough to keep up with these changes.
Despite the different techniques that they employ, the models typically require most of the same basic inputs to create an option's theoretical value. Inputs to the models may vary based on the type of option and the referenced asset.
For example, the basic inputs for American style options on common stock are: whether the option is a put or call, the current asset price, the exercise or strike price, the time to expiration or maturity, the risk-free interest rate, the dividend rate or yield, the cost of carry, and the volatility of the underlying asset. Other option valuation models may require other inputs. For example, Binomial and Trinomial option valuation models also require the user to specify the number of time steps and Merton's Jump Diffusion model requires the user to specify the number of jumps per year.
Uncertain Option Values
Despite new and improved option pricing models, there is still significant uncertainty about what the value of an option is. This uncertainty is resident before the contract is entered into and extends until the date the contract expires, at which point the theoretical value and the market value converge.
Actual option prices may vary significantly from the theoretical values of the option pricing models due to a lack of liquidity. Thin trading may impede price discovery and allow for greater pricing imperfections. This may cause significant pricing distortions on options that do not trade very much such as options on smaller companies, option contracts with expiration dates greater than one year, and deep out-of-the-money contracts.
However there are significant differences between the model values and the market values even when options are heavily traded. Proponents of option pricing-models naturally assume that these differences are caused by different market participants using different assumptions about the inputs to those models.
Since the current stock price, the exercise price, and the time to expiration are fixed, these parameters are not subject to dispute. While the risk-free interest rate and the dividend rate may change, these values do not generally change enough over short-periods of time to cause big changes in option values.
Thus, the parameter most in dispute is the volatility of the underlying stock. Historical volatility can vary significantly based on how the calculation is done and by how many days of historic price changes are used to derive this number.
Implied Volatility
One can take the current market value of an option and the other less contentious model inputs described above and substitute volatilities into the model until it produces a theoretical value that is equal to the market value of the option. This number is called “implied volatility.” In essence, implied volatility is how market participants reconcile actual option prices with the theoretical values derived from the models they use.
One way to describe the difference between historical volatility and implied volatility is to say that market participants think the historical experience of a stock's price changes were abnormal. In effect, they think that the historical experience was more or less volatile than what will happen over the future life of the option.
For those participants who believe that their chosen option pricing model adequately describes the value of an option, implied volatility may be useful for reconciling the model with the market. However, this number is not very meaningful for deep in or out-of-the-money options, where extraordinary amounts of volatility are required to change the option value by relatively small amounts of money.
New Approach Needed
Given how useful they can be, options are not employed nearly as much as they should be. There are several fundamental reasons why options are not used more.
First, option calculations are relatively complicated and difficult for the average investor to understand. The learning curve is steep for most investors, and the details of option usage are difficult to explain to the uninitiated. This lack of understanding makes many investors uncomfortable with using options.
Second, since most options are traded on exchanges, option prices are subject to market distortions which may prevent even the most astute observers from being able to use them effectively. While there is significant trading of stock options at or near-the-money for the largest companies, there may be little or no trading of deep out-of-the-money options on those stocks. Moreover, there is not much liquidity for options that extend beyond one year or for options on the stocks of smaller companies either.
Third, although theoretical models of option valuation may help provide some insight into the pricing of options, they are also problematic. There are now many models to choose from, each with some subtle difference, each meant to address some theoretical problem. Despite all of the advances, there are still significant differences between the model prices and the market price of options. Such differences are confusing to investors. Either the models are wrong or the market is wrong, but how is the investor to know which is right?
Forth, since there is not much of a market for long-duration options such as incentive stock options, one cannot compare the model valuations to the market valuations for such options. Thus, one cannot even demonstrate that the models work as well in such situations as they do on contracts with lesser expiration dates. This is problematic given that current accounting treatment requires companies to ascribe a fair value to incentive stock options.
Meanwhile employees may not attribute much or any value to the options that they are granted because they may not have fully vested, typically have no intrinsic value, and cannot be sold. Moreover, most employees have no understanding of option valuation models.
Fifth, the trading cost of using options can impair the use of deep out-of-the-money options. This is because the expense of trading such options gets too large in relation to the expected value of such options.
Ultimately option usage is curtailed because people do not understand how they work and are suspicious that option prices may be incorrect, regardless of whether they are derived from an option pricing model or the market. In effect, the degree of moneyness, company size characteristics, and near-term expiration dates all limit the potential size of the options market and in turn limit the usefulness of options to investors.